Upload an image, if desired, to Photobucket or Imageshack. (Or any other image hosting site.)
Then go to "My Controls", a hyperlink at the top of the page which is on the same line as your forum handle.
After you click it, it will take you to a new page. On the new page there will be a menu on the left. In that menu an option named "Edit Signature" will be present. Click it.
Type text as required into the box, wrap image links in BB codes.
Click the button down the bottom labeled "Update my Signature".